The loss function for the Cut model depends on the prior \(\pi _0(\theta |\varphi )\)  through the term \( \log p(Y \mid \varphi )\) . In the setting of [1]} this prior dependence could be thought of as another “piece of information” alongside \(Y,Z\) . They write the loss \(l(\xi ;I)\)  where \(\xi =(\varphi ,\theta )\)  is the parameter and \(I=(Y,Z)\)  is the data or “information” informing the parameters. We recover that setup, at least formally, if we write \(I=(Y,Z,\pi _0)\) .
However, [2]} determine valid belief updates for additive losses only (see below), and we will see that the Cut-model loss is not additive, so we can ask, what is the valid belief update for the Cut-model loss? Does it coincide with the Cut-model posterior?
